Through the implicit function theorem (see [1]}, [2]} ), it is known \(k\) -codimensional regular surface can be locally represented as intrinsic graph by a function \(\phi : \mathcal {O} \subset \mathbb {W}\rightarrow \mathbb {M}\) . In [3]} we establish that an appropriate notion of differentiability,
denoted intrinsic differentiability (see Definition REF ), is the additional assumption on \(\phi \)  to obtain the opposite implication. More precisely, a function is intrinsic differentiable if it is well approximated by appropriate linear type functions, denoted intrinsic linear functions. In particular, when \(\mathbb {W}\)  and \(\mathbb {M}\)  are both normal subgroup, this notion corresponds to that of Pansu differentiability.
